Rasch Meta-Metres of Growth for Some Intelligence and Attainment Tests

David Andrich first graduated in Mathematics, then in Education, and received a Fulbright Award for study for his PhD in the Measurement, Evaluation and Statistical Analysis Program at The University of Chicago, United States. His dissertation earned the Susan Colver Rosenberger prize for the best research thesis in the Division of the Social Sciences in 1973. He returned to his appointment at The University of Western Australia, and in 1985 was appointed Professor of Education at Murdoch University in Western Australia, where he held the position of Dean for two periods. In 2007, he returned to The University of Western Australia as the Chapple Professor of Education. He is also Visiting Professor in Educational Assessment at The University of Oxford, United Kingdom. He has also been a visiting Professor at The University of Trento in Italy, and visiting Scholar at the University of Copenhagen and The University of Chicago. He has held major research grants from the Australian Research Council continuously since 1985. David has also conducted commissioned research at both national and state levels, and has been a member of expert advisory committees at national and state levels concerned with large-scale assessments. In 1990, he was elected Fellow of the Academy of Social Sciences of Australia for his contributions to measurement in the social sciences. David is especially known for his work in modern test theory, and in particular Rasch measurement theory, where his work has ranged from the philosophy of measurement, through model exposition and interpretation, to software development. He has also given invited addresses at many conferences and has published in Educational, Psychological, Sociological and Statistical journals. Ida Marais is a Senior Research Fellow at the GSE Psychometric Laboratory, The University of Western Australia. After graduating with a BSc degree majoring in Computer Science and Psychology, she has worked as a computer analyst/programmer for a number of years before being awarded a University of Auckland Doctoral Scholarship and completing a MSc and PhD in Cognitive Psychology. Since then, Ida has been a researcher and lecturer in the fields of Psychology and Education in New Zealand and Australia. Her research activities focus on psychological and educational measurement, especially the measurement of change over time and simulation of data that violate the Rasch model. Ida's current research investigates the issue of maintaining invariant scales in state, national and international level assessments. She has written and continues to develop a data simulation program to study the implications of specific, various violations of responses according to the Rasch model, and the program is used by colleagues worldwide both for research and teaching of the Rasch model. Ida also jointly coordinates postgraduate units in Rasch measurement and supervises postgraduate students in educational measurement. She consults on a number of projects, including the audit of the Undergraduate Medicine and Health Sciences Admission test (UMAT) analysis and the analysis of the Australian national assessment Program (NAPLAN).Sonia Sappl is a Research Assistant at the GSE Psychometric Laboratory, The University of Western Australia. After graduating with a BSc degree majoring in Psychology and Neuroscience, she has completed a Graduate Diploma in Professional Education, and is currently enrolled in a Master of Philosophy (Research) at The University of Western Australia. In her role as a research assistant, Sonia has assisted with the statistical analysis of the National Assessment Program for Science Literacy (NAP-SL) data for calibration and equating.

• Measurement and the study of growth.- Probabilistic fundamental measurement and invariance.- The formulation of a meta-metre in which growth is linear.- Estimates of the rate of growth and initial status.- Application of the modified meta-metre to physical growth.- Growth on the Stanford-Binet test of general intelligence,- Growth in reading and mathematics achievement: ECLS-K study.- Growth in reading and mathematics achievement: NLSY study.- Further examples of growth in reading and mathematics achievement.- Decelerating growth and the setting of an early trajectory.- Summary and discussion.